The distinctive driving force of constraint programming (CP) to solve combinatorial problems has been a privileged access to problem structure through the high-level models it uses. We investigate a richer propagation medium for CP made possible by recent work on counting solutions inside constraints. Beliefs about individual variable-value assignments are exchanged between contraints and iteratively adjusted. Its advantage over standard belief propagation is that the higher-level models do not tend to create as many cycles, which are known to be problematic for convergence. We find that it significantly improves search guidance.